Definition of Conoid:
This is a solid which is also known as cone that is generated by rotating a line segment which is passing through a fixed point and making a constant angle with a fixed line.
In the above figure of right circular cone, here , VO is a fixed line and VA is a rotating line which is making constant angle with VO.The point A would describe a circle with center O such that the line segment VO is perpendicular to the base.
VO is the height "h" and OA is the base radius "r" of the right circular cone VA is the slant height "l" of the right circular cone
It is very clear VAO is right angled triangle and the right angle is at at O.
Since VAO is the right angled triangle by Pythagorean theorem
we have l² = h² + r²
from l² = h² + r² , we can get the value of one of the measurements if we know the value of the other two measurements. For example, if we have the height "h", and the radius "r" of the right circular cone, we can easily determine the value of the slant height "l" of the right circular cone.
If the height and radius of a right circular cone are 4cm and 3cm respectively,find the slant height of the conoid.
Let us plug the known values in to the equation.
l² = h² + r²
l² = 4² + 3²
l² = 16 + 9
l² = 25
so l = 5
that is slant height = 5 cm
Role of radius,slant height and height in finding area and volume:
Measurement of radius,height and slant height plays a vital role in finding curved surface area, total surface area and volumes.
Quote on Mathematics
“Mathematics, without this we can do nothing in our life. Each and everything around us is math.
Math is not only solving problems and finding solutions and it is also doing many things in our day to day life. They are:
It subtracts sadness and adds happiness in our life.
It divides sorrow and multiplies forgiveness and love.
Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?
Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”